A study of the rank force method for structural matrix vibration analysis

Abstract

In the field of structural vibration analysis using finite element techniques and a distributed structural mass representation the displacement method has virtually received complete priority over the force method. To date, no published work has been found on a force approach which adopts an automatic selection of redundancy technique and a distributed structural mass representation. This thesis formulates and investigates such a force method ("The Rank Force Method") and the rank technique is used for automatic selection of redundancies. Distinction is made between static and dynamic redundancy. Procedures for deriving element dynamic flexibility matrices are presented and then applied to give particular dynamic matrices. It is shown that such matrices can be separated into an element static flexibility matrix and an element inverse mass matrix, Endload, beam and rectangular plate elements are considered. Using these elements the rank force method is applied to a number of structural configurations to evaluate their eigenvalues. These results are compared with those obtained using alternative procedures. Element loads and structural reactions for a given frequency and applied loading are also given. A general discussion of the rank force method for vibration analysis is given.

When adopting this force approach for eigenvalue evaluation a highly reduced structural dynamic flexibility matrix can be used, a method is presented and investigated. It is also shown that in vibration analyses the structural reactions need not be imposed until the final stages 6f the force formulation. This is ideal when analysing large practical structures.

All results are obtained by writing the rank force method as a computerized structural analysis research system, such a system is presented and described.

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